Question: Simplify the following expression: $ k = \dfrac{3}{7} + \dfrac{a - 6}{-5a - 4} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5a - 4}{-5a - 4}$ $ \dfrac{3}{7} \times \dfrac{-5a - 4}{-5a - 4} = \dfrac{-15a - 12}{-35a - 28} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{a - 6}{-5a - 4} \times \dfrac{7}{7} = \dfrac{7a - 42}{-35a - 28} $ Therefore $ k = \dfrac{-15a - 12}{-35a - 28} + \dfrac{7a - 42}{-35a - 28} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-15a - 12 + 7a - 42}{-35a - 28} $ $k = \dfrac{-8a - 54}{-35a - 28}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{8a + 54}{35a + 28}$